A metamaterial is a composite structure intended to interact resonantly with electromagnetic radiation at certain wavelengths and composed by individual, typically repeating, units of subwavelength dimensions, whose geometry defines the resonances. Metamaterials are of great interest because they offer the possibility to control and manipulate light in ways that are not achievable using natural materials. The term “light” in this regard is meant to include electromagnetic radiation throughout, among others, the infrared and visible portions of the spectrum.
Various authors have proposed the use of metamaterials for the filtering and modulation of electromagnetic radiation. It has been suggested that metamaterial structures can be scaled for operation in a broad spectral range extending from radio to visible frequencies.
One useful feature of a photonic device such as a filter or modulator is the capacity for dynamic tuning Tuning with an applied voltage is especially desirable, because voltage tuning is generally effective at greater frequencies than thermal and mechanical tuning, and it generally requires less complex circuitry than optical tuning.
Voltage-tunable metamaterial filters have in fact been proposed. For example, it has been known for some time that the metamaterial resonances can be very sensitive to the background dielectric properties of the underlying substrate. Accordingly, one approach has been to form the metamaterial structure on a doped semiconductor substrate, and to apply a reverse bias to deplete the carriers in a surface region near the metamaterial. The resulting change in the dielectric properties of the substrate in turn modifies the resonant behavior of the metamaterial.
Although useful for frequencies in the terahertz (THz) regime or lower, such an approach is not easily scaled to the mid-infrared (MIR) spectral range. One reason is that to be effective, the operative part of the semiconductor substrate would need to exhibit a free-carrier plasma frequency in the MIR range. That could only be done at extremely high carrier concentrations. However, such high carrier densities would limit the depletion region achievable by reverse biasing to an extremely thin layer that in most cases would interact too weakly to provide a useful amount of tuning.
More recently, a mechanism based on inter-subband transitions (ISTs) has been proposed for the voltage tuning of metamaterial structures. It is well known that a homogeneous crystalline semiconductor exhibits a band structure in which one or more valence bands of carrier energy are separated from one or more conduction bands by energy gaps. It is also well known that semiconductors can be engineered to exhibit, at desired levels, accessible energy states that lie within the band gaps. Such energy states are examples of sub-bands. Optical transitions between those sub-bands are examples of ISTs.
The specific ISTs that have been proposed for exploitation in metamaterial devices are transitions between bound states of quantum wells. Skilled artisans have known for many years that a thin epitaxial semiconductor layer of relatively low bandgap enclosed between higher-bandgap layers can define a potential well that can capture electrons. The captured electrons exhibit bound states that typically include a ground state and one or more excited states. Analogous quantum wells for holes are also feasible.
The resonant behavior of a metamaterial resonator (MMR) can be very sensitive to the nearby presence of populated quantum wells. In particular, the respective optical excitations of the MMR and a quantum well can strongly couple, via dipole interactions, when the resonant wavelength of the MMR approaches the absorption wavelength for a transition between bound states of the quantum well. In that circumstance, it is common to encounter “anti-crossing behavior”, in which the respective excitations hybridize so that neither of them is wholly of MMR character or wholly of quantum-well character.
Instead of crossing when the MMRs and quantum wells are tuned toward each other, the energies of the hybrid excitations, which are often referred to as “polaritons”, exhibit anti-crossing behavior. That is, as the MM and IST transition energies are tuned in an attempt to make them mutually resonant, their interaction results in a minimum, but non-zero, energy separation at the point where they would resonate with each other, absent the interaction. As a consequence, the feature consisting of a pair of polariton peaks appears near resonance when the individual MMR and quantum well resonances (at least approximately) coincide, but it is absent when the individual resonances are well separated. Given a tuning mechanism for controllably bringing the respective resonances into and out of coincidence, this phenomenon could be exploited for photonic control applications.
Such a scheme for electrical tuning of planar metamaterials has in fact been proposed. For example, A. Gabbay and I. Brener, “Theory and modeling of electrically tunable metamaterial devices using inter-subband transitions in semiconductor quantum wells,” Optics Express, Vol. 20, No. 6 (12 Mar. 2012) 6584-6597, presents a general scheme for electrically tunable metamaterial devices using ISTs in quantum wells as the substrate on which the metamaterial resonators are fabricated. The same article presents the results obtained through numerical simulation of an MMR array coupled to a stack of quantum well units, in which each unit consisted of a pair of asymmetric coupled gallium arsenide (GaAs) quantum wells separated by aluminum gallium arsenide (AlGaAs) barriers and enclosed between AlGaAs layers.
Electrical tuning was achieved by exploiting the quantum confined Stark effect. That is, the simulations indicated that application of a bias voltage would be able to shift the energies of the ISTs of the coupled quantum wells enough to achieve a useful tuning range. For example, modeling of a single coupled pair of quantum wells predicted that the ground state to first excited state transition could be tuned over a range of about sixty millielectron volts (60 meV) with a biasing electric field strength ranging from −70 to +70 kV/cm. Similarly, simulation of a metamaterial array coupled to a stack of 25 quantum-well pairs showed a tuning range in the quantum well resonance of about 23-32 THz (i.e. an infrared wavelength of 10.9±1.8 μm) for the same range of the biasing field.
Although approaches of the kind reported in Gabbay and Brener (2012) show promise, they have until now suffered the drawback of a very shallow interaction depth between the MMR array and the underlying quantum well stack, because of screening of the bias field by the first highly doped quantum wells. As a consequence, only a few layers in the quantum well stack have an appreciable effect on the spectral behavior of the device. This, in turn, tends to limit the contrast ratio, or modulation depth, that can be achieved when the device is operated as an optical amplitude modulator or tunable filter.
Thus, there remains a need for improved electrically tunable, resonant metamaterial photonic devices that can achieve greater modulation depths or spectral shifts, particularly for operation at infrared wavelengths.